Terahertz quantum cascade (QC) lasers generally use sub-wavelength metallic and/or plasmonic waveguiding techniques, which can lead to divergent poor-quality beams. Achieving a high quality beam, such as symmetric, directive, diffraction-limited, and non-astigmatic, is thus a challenge for QC lasers. The scheme of vertical external cavity surface emitting laser (VECSEL) has been a solution for some types of semiconductor lasers. In a typical VECSEL configuration, a quantum well (or dot) of semiconductor active medium is grown monolithically with a distributed Bragg reflector. When optically pumped over a large area, the semiconductor medium forms an active reflector as part of an external laser cavity, which can be readily engineered to support solely or primarily the fundamental Gaussian mode so as to provide a circular output beam with diffraction-limited beam quality—even for high powers. However, a conventional design of surface emission seems to be incompatible with QC lasers. In a QC laser, the optical gain is based upon intersubband transitions of electrons within planar quantum wells. These transitions obey a “intersubband selection rule” by which solely or primarily light with the electric field polarized along the growth direction of the wells can be emitted. Therefore, the conventional design of VECSEL cannot be readily implemented for QC lasers since the polarization of light in the cavity would not couple with the QC gain transitions.
Currently, Bragg scattering is used to redirect the in-plane radiation of terahertz QC lasers to achieve more directive surface emitting beams. For example, 2nd order distributed feedback (DFB) cavities and photonic crystal (PhC) cavities have been used for surface emission in QC lasers which resulted in about 9°×6° divergence; 3rd order DFB cavities have been used for end-fire emission in QC lasers which resulted in a 6°×11° divergence. The 2nd order DFB and PhC cavities use surface emitting Bragg laser cavities to obtain a large radiating aperture for good beam quality. Further decreasing the beam divergence along both axes involves either on-chip phase locking between large numbers of 2nd order DFB array elements, which adds complexity and might cause side lobes in the beam pattern due to the grating diffraction (array ridges' width is usually larger than the free-space wavelength), or a large PhC cavity dimension, which degrades the temperature performance. The 3rd order DFB cavities operate as end-fire antennas, which allow a directive beam (e.g., far-field divergence of about 10°) from a laser ridge with subwavelength transverse dimensions. However, since the beam divergence from a 3rd order DFB laser scales with a square root of the ridge length L (i.e., L−1/2), improvement in beam directivity might involve inconveniently long ridges (e.g., a 6°×11° far-field was achieved using a 5.7 mm long ridge), which are subject to spatial hole burning and become increasingly difficult to phase match. It is against this background that a need arose to develop the embodiments described in this disclosure.